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The figure drawn below gives the velocity graphs of two vehicles A and B. The straight line OKP represents the velocity of vehicle A at any instant, whereas the horizontal straight line CKD represents the velocity of vehicle B at any instant. In the figure, D is the point where perpendicular from P meets the horizontal line CKD such that \(PD=\dfrac{1}{2}LD\) : What is the ratio between the distances covered by vehicles A and B in the time interval OL?

The figure drawn below gives the velocity graphs of two vehicles A and B. The straight line OKP represents the velocity of vehicle A at any instant, whereas the horizontal straight line CKD represents the velocity of vehicle B at any instant. In the figure, D is the point where perpendicular from P meets the horizontal line CKD such that \(PD=\dfrac{1}{2}LD\) : What is the ratio between the distances covered by vehicles A and B in the time interval OL? Correct Answer 3 ∶ 4

Concept used:

Area of rectangle = Length × breadth 

Area of triangle = (1/2) × Base × Height 

Distance covered 'S' = Area of (V - T) graph

Calculations:

Displacement of vehicle A = Distance covered by A = Area of ΔOPL 

⇒ (1/2) × OL × LP

⇒ (1/2) × OL × (LD + PD)

⇒ (1/2) × OL × (LD + LD/2)

⇒ (1/2) × OL × 3LD/2 

⇒ 3/4 × OL × LD 

Displacement of vehicle B = Distance covered by B = Area of rectangle OLDC

⇒ OL × LD 

The ratio between the distances covered by vehicles A and B in the time interval OL

⇒ (Displacement of vehicle A)/Displacement of vehicle B

⇒ ((3/4) × OL × LD)/(OL × LD)

⇒ 3/4 

∴ The ratio between the distances covered by vehicles A and B in the time interval OL is 3 ∶ 4

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